An Outdoor Thermal Comfort Index for the Subtropics

PLEA2009 - 26th Conference on Passive and Low Energy Architecture, Quebec City, Canada, 22-24 June 2009 

An Outdoor Thermal Comfort Index for the Subtropics 

LEONARDO MARQUES MONTEIRO, MARCIA PEINADO ALUCCI 

Faculty of Architecture and Urbanism, University of Sao Paulo, Sao Paulo, Brazil 

ABSTRACT: This paper presents a research that proposes a thermal comfort index, allowing the verification of the 

thermal adequacy of outdoor spaces in the subtropics. The method adopted is experimental inductive, by means of field 

research of a total of ninety-eight micro-climatic situations and over two thousand and five hundred applied 

questionnaires of thermal sensation perception and preference. Deductive method is also applied, by means of regression 

analysis, considering seventy-two different micro-climatic conditions. The significance of the results is verified by 

comparison with the ones obtained by simulation of different predictive models and respective indexes, considering the 

results from twenty-six different micro-climatic conditions gathered in different urban situations from the previous survey. 

The results from the proposed equation, compared with those from the others predictive models, showed that, for the 

specific subtropical microclimatic conditions, they present better correlations with the data gathered. Concluding, the 

methods used provided a simple, easy-to-use and reliable thermal comfort index to assess outdoor thermal comfort in the 

subtropical climate. 

Keywords: thermal comfort, outdoors, predictive models, equivalent temperature 

INTRODUCTION 

Thermal comfort assessment in outdoor spaces requires 

the comprehension of additional factors, which are not 

taken into account in a typical indoor situation. Shortwave 

radiation and winds, considerable sweating rates or 

variable clothing, different human activities and 

expectations, among other factors, bring more 

complexity to the analysis. This paper presents a research 

that proposes a thermal comfort index, allowing the 

verification of the thermal adequacy of outdoor spaces in 

the subtropics. The method adopted is experimental 

inductive, by means of field research of micro-climatic 

variables and subjective answers, and deductive, by 

means of regression analysis. The significance of the 

results is verified by comparison with the ones obtained 

by simulation of predictive models. 

BACKGROUND 

This study considered twenty-two predictive models and 

their indexes. They will be here briefly presented in order 

to perform later correlation of their results with the 

results of the empirical research. 

Houghten et al. [1], of ASHVE laboratories, propose, 

in 1923, the Effective Temperature (ET), as determined 

by dry and wet bulb temperature and wind speed. Vernon 

& Warner [apud 2], in 1932 propose the Corrected 

Effective Temperature (CET) substituting dry bulb 

temperature with globe temperature. 

Siple & Passel [3], in 1965, develop the Wind Chill 

Temperature (WCT) from the data obtained with 

experiences in Antarctica. 

Belding & Hatch [4], in 1965, propose the Heat 

Stress Index (HSI), relying on a thermal balance model 

with empirical equations for each exchange. 

Yaglou & Minard [5], in 1957, propose the Wet Bulb 

Globe Temperature (WBGT). ISO 7243:1989 [6] gives 

an alternate equation for situations under solar radiation. 

Gagge [7], in 1967, presents the New Standard 

Effective Temperature (SET*), defining it as the air 

temperature in which, in a given reference environment, 

the person has the same skin temperature (tsk) and 

wetness (w) as in the real environment. 

Givoni [8], in 1969, proposes the Index of Thermal 

Stress (ITS), which considers the heat exchanges, 

metabolism and clothes. Originally, it did not consider 

the radiation exchanges. 

Masterton & Richardson [9], in 1979, propose the 

Humidex, an index calculated based on air temperature 

and humidity. It is used by the Environment Canada 

Meteorological Service to alert people of the heat stress 

danger. 

Jendrizky et al. [10], in 1979, developed the Klima 

Michel Model (KMM). It is an adaptation of Fanger’s


model [11], with a short wave radiation model, computed 

in the mean radiant temperature. 

Vogt [12], in 1981, proposes the evaluation of 

thermal stress through the required sweat rate (Swreq). 

This index was adopted by ISO 7933:1989 [13]. 

Dominguez et al. [14], in 1992, present the research 

results of the Termotecnia Group of Seville University, 

also based on Vogt [12]. The authors accept low sweat 

rates according to the conditioning required. 

Brown & Gillespie [15], in 1995, propose an outdoor 

Comfort Formula based on thermal budget (S) with some 

particularities in its terms. 

Aroztegui [16], also in 1995, proposes the Outdoor 

Neutral Temperature (Tne), based on Humphreys [17] 

and taking into account the solar radiation and air speed. 

Blazejczyk [18], in 1996, proposes the Man- 

Environment Heat Exchange model (Menex), based on 

thermal balance. The author proposes three criteria, 

which are supposed to be considered as a whole: Heat 

Load (HL), Intensity of Radiation Stimuli (R’) and 

Physiological Strain (PhS). He also proposes the 

Subjective Temperature Index (STI) and the Sensible 

Perspiration Index (SP). DeFreitas [apud 19], in 1997, 

presents the Potential Storage Index (PSI) and the Skin 

Temperature Equilibrating Thermal Balance (STE), both 

using the Menex Model. 

Höppe [20], in 1999, defines the Physiological 

Equivalent Temperature (PET) of a given environment as 

the equivalent temperature to air temperature in which, in 

a reference environment, the thermal balance and the 

skin and core temperatures are the same of that found in 

the given environment. 

Givoni & Noguchi [21], in 2000, describe an 

experimental research in a park in Yokohama, Japan, and 

propose the Thermal Sensation Index (TS). 

Bluestein & Osczevski [22], in 2002, propose the 

New Wind Chill Temperature (NWCT), through a 

physical modelling of a face exposed to wind. 

Nikolopoulou [23], in 2004, presents the works 

developed by the project Rediscovering the Urban Realm 

and Open Spaces (RUROS), proposing the actual 

sensation vote (ASV). 

EMPIRICAL DATA 

The procedures were done following guidelines and data 

from [24, 25, 26, 27, 28]. 

On the field researches, seventy-two different microclimatic 

scenarios were considered and one thousand and 

seven hundred and fifty questionnaires were applied 

during summer and winter of two consecutive years, in 

the city of Sao Paulo, Brazil. The procedures are briefly 

presented in the following paragraphs. 

For the measurements and application of 

questionnaires, three bases were set: the first one under 

open sky, the second one shaded by trees, and the third 

one under a tensioned membrane structure. In each one 

of the three bases, micro-climatic variables (mean radiant 

temperature, air temperature, air humidity and wind 

speed) were measured and a hundred and fifty people 

answered a questionnaire, in six different hours of the 

day. These people came from different regions of Brazil. 

Further studies will consider not only the results from 

acclimatized ones, but also comparatively the results 

from those who were not acclimatized. 

The questionnaire considered questions of personal 

characteristics (sex, age, weight, height), acclimatization 

(places of living and duration) and subjective responses 

(thermal sensation, preference, comfort and tolerance). 

Pictures were taken of everyone who would answer the 

questionnaire, in order to identify clothing and activity. 

A forth base, at 10m high, was set for measuring 

meteorological parameters (global radiation and wind 

speed). 

The equipment used in each base was the following. 

Under open sky: meteorological station ELE model 

EMS, data logger ELE model MM900 EE 475-016. 

Shaded by trees: meteorological station Huger Eletronics 

model GmbH WM918 and personal computer for data 

logging. Under tensioned membrane structure: station 

Innova 7301, with modules of thermal comfort and 

stress, and data logger Innova model 1221. At 10m high: 

meteorological station Huger Eletronics model GmbH 

WM921 and a piranometer Eppley. 

In each base, globe temperature was also measured 

through 15cm grey globes and semiconductor sensors, 

storing the data in Hobo data loggers. The measurements 

were done in intervals of one second, and the storage was 

done in intervals of one minute, considering the average 

of measurements. 

The limits in which the empirical data were gathered 

are: air temperature (ta) = 15°C~33°C; mean radiant 

temperature (mrt) = 15°C~66°C; relative humidity (rh) = 

30%~95%; wind speed (va) = 0,1m/s~3,6m/s. It should 

also be mentioned that, although it is not a limiting factor 

for normal situations, the maximum and minimum 

clothing thermal insulation values found were 0,3 and 1,2 

clo, with mean values between 0,4 and 0,9 clo. 

Considering the Typical Reference Year (TRY) [29] 

for Sao Paulo, the ranges presented represent 92% of the


general climatic situations during day time. On the other 

hand, if it is necessary to make an extrapolation, it must 

be done carefully and would better be object of further 

researches. 

MODELLING 

The multiple linear regression to be presented was 

obtained considering the data from the seventy-two 

microclimatic situations, regarding the application of one 

thousand and seven hundred and fifty questionnaires. 

tsp= -3,557 + 0,0632 · ta + 0,0677 · mrt + 

+ 0,0105 · ur - 0,304 · va [1] 

with: r= 0,936; r 2 = 0,875; r 2 aj= 0,868; se= 0,315; P< 

0,001. 

where: tsp= thermal sensation perception 

[dimensionless], ta = air temperature [ o C], mrt = mean 

radiant temperature [ o C], rh = relative humidity [%], v = 

air velocity [m/s] 

Considering the thermal sensation perception (tsp), 

following the categories of the applied questionnaires, 

result from -0,5 to 0,5 means neutrality; from 0,5 to 1,5 

means warm; from 1,5 to 2,5 means hot; above 2,5 

means very hot; from -0,5 to -1,5 means cool; from -1,5 

to -2,5 means cold; and below -2,5 means very cold. 

Table 1 presents a statistic resume of the constant and 

the four dependent variables and Table 2 presents the 

analysis of variance. 

Table 1: Statistic summary of the constant and the four 

dependent variables 

c se t p VIF 

ct -3,557 0,249 -11,17


Table 3: Limit values for microclimatic variables 

variable min max 

ta ( o C) 15,1 33,1 

mrt ( o C) 15,5 65,5 

rh (%) 30,9 94,7 

va (m/s) 0,1 3,6 

TEP ( o C) 13,7 45,3 

VERIFICATION 

Three criteria were established for comparing the 

simulation results with the field research results aiming 

to verify the significance of the results provided by the 

new proposed predictive model. The first criterion is the 

correlation between the results of the model parameter 

and the results of the thermal sensation responses 

obtained in the field study. The second criterion is the 

correlation between the results of the index and the 

results of the thermal sensation responses obtained in the 

field study. The last one is the percentage of correct 

predictions. 

Concerning the indexes based on equivalent 

temperatures, the criterion for interpretation of the 

indexes used was the one by De Freitas [19]. Yet the 

author proposes this one only for effective temperatures, 

it was used for other equivalent temperatures because no 

other references were found; except for STI, for which 

was used Blazejczyk [18]. 

All the criteria are based on results concerning new 

empirical field researches, performed during summer and 

winter, in three different locations, in another 

neighbourhood of Sao Paulo, using the same procedures 

established before, and considering twenty-six new 

micro-climatic scenarios and the mean thermal sensation 

responses for each one of this scenarios (eight hundred 

and fifty eight applied questionnaires). 

Aiming better results to the specific evaluation of 

open spaces of Sao Paulo, a calibration was performed in 

order to fit the results from the simulations to the results 

found in the empirical researches. In order to do so, each 

index was linguistically compared to seven values (the 

same used in the field researches): three positive ones 

(warm, hot, very hot), three negative ones (cool, cold, 

very cold) and one of neutrality (negative values do not 

apply for models that consider only hot environments). 

The calibration was done through iterative method, 

changing the range limits of each index in order to 

maximize the correlation between its results and those 

found in the empirical researches. The calibration could 

be done, also iteratively, to maximize the percentage of 

correct predictions. However, it was assumed that is 

more important to assure the maximization of the 

correlation between the results of the index and those 

from empirical data, once this correlation expresses the 

tendency of correctly predicting other situations. 

RESULTS 

Table 4 presents the final results considering the 

comparison criteria presented. This table presents the 

correlation modules between field study results and 

simulation results, without and with the calibration 

process presented. 

Table 4: Correlation between field study and simulation results 

Index C Co Po Cc Pc 

ET* 0,73 0,59 44% 0,71 72% 

CET* 0,89 0,77 11% 0,85 81% 

OT 0,72 0,69 47% 0,72 75% 

EOT* 0,70 0,66 42% 0,73 75% 

WCTI 0,69 0,64 31% 0,74 78% 

HSI 0,83 0,72 68% 0,89 81% 

WBGT 0,86 - - 0,86 89% 

SET* 0,89 0,84 28% 0,86 86% 

ITS 0,84 0,75 62% 0,89 86% 

HU 0,74 0,70 69% 0,78 81% 

PMV 0,87 0,82 65% 0,83 86% 

Swreq 0,87 - - 0,86 83% 

W 0,86 - - 0,86 83% 

Swreq’ 0,89 0,83 72% 0,89 86% 

S’ 0,89 0,65 61% 0,87 83% 

Tne 0,88 0,70 33% 0,89 86% 

HL 0,89 0,76 62% 0,88 86% 

PhS 0,81 0,71 28% 0,89 86% 

R’ 0,86 0,76 69% 0,86 83% 

STI 0,87 0,79 53% 0,82 78% 

SP 0,89 0,82 78% 0,89 86% 

ECI 0,78 0,72 42% 0,80 81% 

PSI 0,89 0,86 78% 0,88 83% 

STE 0,79 0,71 58% 0,81 83% 

PET 0,89 0,78 31% 0,89 86% 

TS 0,87 0,84 78% 0,89 89% 

NWCTI 0,62 0,60 22% 0,71 72% 

ASV 0,85 0,77 76% 0,89 86% 

TEP 0,94 - - 0,94 96% 

where: C= Correlation with the model parameter; 

Co= Correlation with the original index without 

calibration; Po= Percentage of correct predictions 

without calibration; Cc= Correlation with the index with 

calibration; and Pc= Percentage of correct predictions 

with calibration. 

DISCUSSION 

Considering Table 4, one may observe that the best 

results without calibration are provided by the Potential 

Storage Index (PSI), calculated using the MENEX model 

proposed by Blazejczyk [18]. This index presented


correlations of 0,89 and 0,86; respectively for its model 

parameter and its original index. The percentage of 

correct predictions, also without calibration was one of 

78%, one of the highest among the original indexes. 

Table 5 shows PSI interpretative ranges, which is 

originally presented by [18]. 

Table 5: Potential Storage Index (PSI) 

PSI (W/m 2 ) Interpretation 

< -184 very hot 

-184 ~ -111 hot 

-110 ~ -50 warm 

-49 ~ 16 neutral 

17 ~ 83 cool 

84 ~161 cold 

> 162 very cold 

Following Table 4, one may affirm that, before the 

proposal of the Temperature of Equivalent Perception 

(TEP), for the specific case of evaluating outdoor spaces 

on the subtropics, the best index would be the Perceived 

Equivalent Tempeature, calculated using the MEMI 

model proposed by Hoppe [20]. Although it provided 

poorer results considering the first interpretative ranges, 

with the calibration process the new ranges provided the 

best results among the studied indexes: correlations of 

0,89 and 0,89; respectively for the model parameter and 

the calibrated index. The percentage of correct 

predictions, with calibration, was 86%. Table 6 presents 

the calibrated ranges proposed by this research to 

interpretation of the Physiological Equivalent 

Temperature (PET), by [20]. 

Table 6: Physiological Equivalent Temperature (PET) 

PET ( o C) Interpretation 

> 43,0 very hot 

31,0 ~ 43,0 hot 

26,0 ~ 31,0 warm 

18,0 ~ 26,0 neutral 

12,0 ~ 18,0 cool 

4,0 ~ 12,0 cold 

< 4,0 very cold 

Keep on following Table 4, one may observe that the 

results of the proposed Temperature of Equivalent 

Perception (TEP) provides better results than all the other 

indexes, even when compared with the results form the 

calibrated indexes. Its correlations are of 0,94 for the 

model parameter and 0,94 for the index. The percentage 

of correct predictions achieved 96%, the highest among 

all the results. 

In the topic about modelling, it was argued that the 

advantage of equivalent temperatures is the intuitive 

interpretation of their values. On the other hand, it is also 

interesting to provide an interpretative range, since the 

intuitive interpretation is only possible after the 

exposition to several environments and their respective 

equivalent temperatures. Thus, Table 7 presents the 

interpretative ranges for the Temperature of Equivalent 

Perception (TEP), considering the results found in the 

empirical researches. 

Table 7: Temperature of Equivalent Perception (TEP) 

TEP ( o C) Sensation 

> 42,5 very hot 

34,9 ~ 42,4 hot 

27,3 ~ 34,8 warm 

19,6 ~ 27,2 neutrality 

12,0 ~ 19,5 cool 

4,4 ~ 11,9 cold 

< 4,3 very cold 

One may observe that the criteria used to evaluate the 

model predictions allow successive verifications. The 

first correlation verifies the possible potential of the 

model. In other words, it verifies the sensibility of the 

model, showing how well the model parameter results 

vary in function to variations of thermal responses. The 

second correlation does the same, but specifically with 

the interpretation criteria of the indexes. The final 

criterion gives the percentage of correct predictions, 

telling how well the model is performing. 

Considering the calibration, we can observe that it 

provides better correlation with the new empirical data 

gathered and consequently greater percentage of correct 

predictions. Considering the results found, it is more 

interesting to use a model with a better first correlation 

(the correlation between the model parameter and the 

field subject responses) than a one with a greater 

percentage of correct predictions but with a poor first 

correlation, because a good first correlation means that 

the models, once calibrated with empirical data, has a 

good potential to correctly predict the thermal sensations. 

As one may see, the Temperature of Equivalent 

Perception (TEP), proposed in this work, presents the 

highest correlation between the model parameter and the 

field subject responses, leading also to the highest 

correlation between the index and the field subject 

responses. Finally, it presents also the best results in term 

of percentage of correct predictions. One may also notice 

that, before proposing the Temperature of Equivalent 

Perception, the best results would be given by the 

Potential Storage Index (PSI), calculated using the 

MENEX model proposed by Blazejczyk [18], or by the 

Physiological Equivalent Temperature (PET), calculated 

using the MEMI model proposed by Hoppe [18]. 

One may see that both indexes are estimated by 

means of a thermo-physiological balance model, which 

needs several iterations to provide reliable results. The 

Temperature of Equivalent Perception (TEP) not only 

presented better results compared to the empirical data


gathered, but also provides a simpler model to estimate 

outdoor thermal comfort, since it relies on only one 

multiple linear equation. 

FINAL CONSIDERATION 

The contribution of this paper is to provide a thermal 

comfort index which can be properly used for predicting 

thermal comfort in outdoor spaces in a subtropical 

climate. The experimental comparative study of different 

outdoor thermal comfort predictive models allowed the 

verification of the results. Comparing the results from the 

equation generated from multiple linear regression 

analysis to the ones from the predictive models (even 

from the calibrated ones), one may observe that the 

equation found, which culminated in the proposal of the 

Temperature of Equivalent Perception (TEP), presents 

better correlations with the data gathered in new 

scenarios. Concluding, the research provided a simple, 

easy-to-use and reliable index to assess thermal comfort 

in outdoor spaces in a subtropical climate. 

ACKNOWLEDGMENTS. The authors would like to 

thank the Fundacao de Amparo a Pesquisa do Estado de 

Sao Paulo (FAPESP), for the financial support in this 

research. 

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An Outdoor Thermal Comfort Index for the Subtropics

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